Appendix 1 to Chapter 5 Models of Asset Pricing
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-2 Expected Return
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-3 Expected Return: Example
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-4 Standard Deviation of Returns
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-5 Standard Deviation of Returns: Example
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-6 Benefits of Diversification Diversification is almost always beneficial to the risk-averse investor since it reduces risk unless returns on securities move perfectly together The less the returns on two securities move together, the more risk reduction there is from diversification
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-7 Diversification and Beta I
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-8 Diversification and Beta II
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-9 Diversification and Beta II (cont’d)
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-10 Diversification and Beta III
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-11 Diversification and Beta IV
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-12 Systematic and Nonsystematic Risk I
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-13 Systematic and Nonsystematic Risk II
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-14 Systematic and Nonsystematic Risk II (cont’d)
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-15 Capital Asset Pricing Model (CAPM) Shaded area shows combinations of standard deviation and expected return for various portfolios with differing levels of risk The most attractive combinations for the risk-averse investor are on the heavy line, the efficient portfolio frontier Choosing different combinations an investor can form a portfolio that lies anywhere on the line A-C
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-16
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-17 Capital Asset Pricing Model (CAPM) (cont’d) M is chosen so that it is tangent to the efficient portfolio frontier The line is the opportunity locus, the best combination of standard deviations and expected returns available to the investor Assumes that all investors have the same assessment of the expected returns and standard deviations of all assets Therefore portfolio M and the market portfolio are the same
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-18 CAPM Equation
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-19 Security Market Line The expected return that the market sets for a security given its beta Beta of 1.0 marginal contribution to a portfolio’s risk is the same as the market so it should be priced to have the same expected return as the market portfolio An asset should be priced so that it has a higher expected return not when it has a greater risk in isolation, but rather when its systematic risk is greater
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-20
Copyright © 2007 Pearson Addison-Wesley. All rights reserved. 5A(1)-21 Arbitrage Pricing Theory There can be several sources of systematic risk that cannot be eliminated through diversification Factors related to inflation, aggregate output, default risk premiums and/or the term structure of interest rates Same basic conclusion as CAPM—an asset should be priced so that it has a higher expected return when its systematic risk is greater